The main objective of this research is to develop a methodology that can be used to optimally combine geodetic data for empirical modelling of the temporal variations of the geoid caused by the slow dynamic process of glacial isostatic adjustment of the Earth. A dynamic geoid model is needed for establishing a modem dynamic geoid-based vertical datum for Canada. By correcting the geoid for the secular temporal variations, a reference surface for orthometric heights free from systematic effects due to geodynamics will be maintained. To provide a centimetre level of accuracy for precise surveying activities, corrections should be applied generally at a ten-year time interval. Models of the temporal variations of orthometric heights are another important outcome required for ensuring consistency between the dynamic vertical reference surface and gravity related heights.

The sub-objectives of this research are (i) developing a general framework for combining terrestrial and space-borne data including GRACE, GPS, tide gauge/altimetry, and absolute gravimetry data, (ii) implementing data-driven statistical approaches for modelling temporal variations of the geoid and heights, and (iii) delineating practical considerations for implementing the dynamic geoid model as a dynamic vertical reference surface.

The developed methodology is applied, for the first time, to combine GRACE-observed rates of vertical deformation with terrestrial data. The modeled temporal variations of the geoid agree within 0.1 - 0.2 mm/yr with glacial isostatic model predictions based on the ICE-4G model in the areas with a peak geodynamic signal. Making use of robust leastsquares procedures combined with variance component estimation, reliable constraints for geodynamic modelling free from the influence of erroneous observations and reliably estimated error bounds of the empirical rates of crustal displacement are provided. An important outcome of this research is the use of the developed statistical tools as a necessary step towards combining geodynamic modelling of glacial isostatic adjustment with the empirical statistical approach in a rigorous dynamic-based procedure.